Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C24 |
| direct product | C73×#23751 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C73 | C2×#124 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| socle | C2×C73 | C2×#400 |
| prime radical | C24×C73 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C73 ◁ C23×C4×C73 ◁ G | |
664 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 4 generators on 105 points:
(1,2,5,9,6,10,12,21)(3,11,14,23,15,26,20,7)(4,16,19,30,18,8,24,25)(13,27,28,29,17,31,32,22)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105);(1,3,12,14,6,15,5,20)(2,7,21,11,10,23,9,26)(4,17,24,32,18,13,19,28)(8,22,30,27,16,29,25,31);(1,4,5,19,6,18,12,24)(2,8,9,25,10,16,21,30)(3,13,14,28,15,17,20,32)(7,22,11,27,23,29,26,31);(4,18)(8,16)(13,17)(19,24)(22,29)(25,30)(27,31)(28,32)3358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 16739);